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Ghomanjani, F.; Kılıçman, A.; Akhavan Ghassabzade, F.

Numerical solution of singularly perturbed delay differential equations with layer behavior. (English) Zbl 1474.65192

Abstr. Appl. Anal. 2014, Article ID 731057, 4 p. (2014).
Summary: We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into \(k\) subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree \(n\) and determined Bezier curves on any subinterval by \(n + 1\) control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.

Cited in 2 Documents

MSC:

65L03 Numerical methods for functional-differential equations
34K10 Boundary value problems for functional-differential equations
65L11 Numerical solution of singularly perturbed problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
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\textit{F. Ghomanjani} et al., Abstr. Appl. Anal. 2014, Article ID 731057, 4 p. (2014; Zbl 1474.65192)
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References:

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